Parity anomaly governs the thermal Hall response of chiral superconductivity in rhombohedral graphene above and below Tc
Abstract
Chiral superconductivity has recently been confirmed in rhombohedral tetra- and pentalayer graphene near the BCS--BEC crossover, but no theory tells the experimentalist what thermal Hall response to expect, or why any signal should persist above the phase-coherence temperature Tc. We show that the parity anomaly of (2+1)-dimensional field theory fixes the answer exactly, at all temperatures, with no free parameters: κxy/T = (π2 kB2/6h) CBdG tanh[Δ(T)/(2kBT)], where CBdG is the BdG Chern number and Δ(T) is the fermionic excitation gap. The BCS--BEC two-gap relation Δ2 = Δsc2 + Δpg2 makes the same formula govern both the condensate and pseudogap regimes, so the signal onsets at the pair-formation temperature T* rather than at Tc. Coleman--Hill non-renormalization and the c1 = 0 theorem protect this result against interactions and finite-size artefacts. Three independent numerical validations confirm the topological input at machine precision (FHS Chern numbers, Wilson-loop c1 = 0 test) and at the many-body level (DMRG on 28 converged ground states, including the real-space p+ip signature arg𝒜y − arg𝒜x = −π/2 recovered to 10−14). The theory delivers an immediate falsifiable test that requires no new experimental apparatus: the sign of κxy/T below Tc must equal the sign of the anomalous Hall resistance Rxy already measured above Tc, and four further predictions accessible by dilution-refrigerator nano-calorimetry on existing devices.
Related
- Phonon-Mediated Superconductivity near Phase Boundaries in Rhombohedral Multilayer Graphene
- Chiral Superconductivity Adjacent to a Wigner Crystal in Rhombohedral Graphene
- Valley-Helical Superconductivity Driven by Repulsion and Quantum Geometry: Applications to Time-Reversal Symmetric Rhombohedral Graphene
- Spin-polarized Superconductivity and High-Chern Insulators in Twisted Rhombohedral Graphene Family
- Coexistence of Superconductivity and Chern insulators with |C| ≥ 1 in twisted rhombohedral bilayer-trilayer graphene
BibTeX
@misc{ghosh2026parity,
title = {{Parity anomaly governs the thermal Hall response of chiral superconductivity in rhombohedral graphene above and below $T_c$}},
author = {Kumar Ghosh},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18954},
eprint = {2609.18954},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18954},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Parity anomaly governs the thermal Hall response of chiral superconductivity in rhombohedral graphene above and below T_c
AU - Kumar Ghosh
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.18954
UR - https://arxiv.org/abs/2609.18954
AB - Chiral superconductivity has recently been confirmed in rhombohedral tetra- and pentalayer graphene near the BCS--BEC crossover, but no theory tells the experimentalist what thermal Hall response to expect, or why any signal should persist above the phase-coherence temperature T_c. We show that the parity anomaly of (2+1)-dimensional field theory fixes the answer exactly, at all temperatures, with no free parameters: κ_xy/T = (π^2 k_B^2/6h) C_BdG tanh[Δ(T)/(2k_BT)], where C_BdG is the BdG Chern number and Δ(T) is the fermionic excitation gap. The BCS--BEC two-gap relation Δ^2 = Δ_sc^2 + Δ_pg^2 makes the same formula govern both the condensate and pseudogap regimes, so the signal onsets at the pair-formation temperature T^* rather than at T_c. Coleman--Hill non-renormalization and the c_1 = 0 theorem protect this result against interactions and finite-size artefacts. Three independent numerical validations confirm the topological input at machine precision (FHS Chern numbers, Wilson-loop c_1 = 0 test) and at the many-body level (DMRG on 28 converged ground states, including the real-space p+ip signature arg𝒜_y − arg𝒜_x = −π/2 recovered to 10^−14). The theory delivers an immediate falsifiable test that requires no new experimental apparatus: the sign of κ_xy/T below T_c must equal the sign of the anomalous Hall resistance R_xy already measured above T_c, and four further predictions accessible by dilution-refrigerator nano-calorimetry on existing devices.
ER -